Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors' approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (''Beyond Formulas'') that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, ''Today in Mathematics,'' stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.

Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series Estimating the Sum of an Alternating Series 9.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Test 9.6 Power Series 9.7 Taylor Series Representations of Functions as Series Proof of Taylor's Theorem 9.8 Applications of Taylor Series The Binomial Series 9.9 Fourier Series

Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors' approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (''Beyond Formulas'') that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, ''Today in Mathematics,'' stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.

Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series Estimating the Sum of an Alternating Series 9.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Test 9.6 Power Series 9.7 Taylor Series Representations of Functions as Series Proof of Taylor's Theorem 9.8 Applications of Taylor Series The Binomial Series 9.9 Fourier Series